Answer:
184 in.^2
Step-by-step explanation:
The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.
area of circle
[tex]A_{circle} = \pi r^2[/tex]
[tex] \pi r^2 = 46 [/tex]
[tex] r^2 = \dfrac{46}{\pi} [/tex]
[tex] r = \sqrt{\dfrac{46}{\pi}} [/tex]
[tex] r = 3.83 ~in.[/tex]
surface area of sphere
[tex] SA = 4 \pi r^2 [/tex]
[tex] SA = 4 \times \pi \times (3.83)^2 [/tex]
[tex] SA = 184~in.^2 [/tex]
